can be understood in terms of pseudo-triangulations. From this characterization we derive an effective procedure to generate infinitely many planar periodic expansive designs. We also present a few principles to generate infinite auxetic families in higher dimensions. We illustrate these techniques with an abundance of new auxetic blueprints in dimension three, which is most important for metamaterial design.

This talk will give a constructive approach to exploring tangled filaments in a periodic box, where hyperbolic line packings decorate triply-periodic minimal surfaces. A particular arrangement of tangled filaments will be explored in the context of keratin filaments in human skin cells, as well as the broader idea of geometric form as a consequence of the restoring force of a liquid. Finally, I will connect the idea of filament tangling with framework material design.

Shape and structure challenges from users of the 3D micron-scale imaging beamline at the Advanced Light Source
Dilworth Parkinson (Lawrence Berkeley National Lab)

Location

MSRI: Simons Auditorium

Video

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Abstract

Beamline 8.3.2 at the Advanced Light Source is an instrument for Hard X-ray Micro-Tomography, providing its users with micron-resolution 3D images, which they analyze by measurement and modeling of the imaged structures. I will present examples of the types of challenges faced during this analysis, and the questions that can be answered in areas including including earth science (why does "flexible sandstone" bend? can shape predict CO2 flow in sandstone?), biology (what is the path of CO2 and H2O through a leaf? why did spiders evolve different head shapes?), and materials science (why do cracks form in the shape they do during processing and then loading of ceramic matrix composites?).

Applications of convnets to microstructural description and material design
Daniela Ushizima (Lawrence Berkeley National Lab; University of California; BIDS)

Location

MSRI: Simons Auditorium

Video

Abstract

Advances in imaging for the design and investigation of materials have been remarkable: the growth of x-ray brilliance was 18 orders of magnitude in 5 decades, and extremely quick snapshots have enabled description of dynamic systems at the atomic scale. From industry to national laboratories, shape and structural properties of new compounds imaged through x-rays are used to measure the function and resilience of new materials. What drastically changed is the frequency in which this data modality is collected and used as a key scientific record, which is unprecedented. One of the main challenges is how to couple increasing data rate experiments to new Data Science methods in support of more automated analytical tasks for scientific discovery. Recent efforts in machine learning applied to data representation and structural fingerprints have streamlined sample sorting and ranking, including the identification of special materials configurations from million-sized image databases. Methods such as convolutional neural networks have allowed automated characterization of abstract pictures, such as scattering patterns, based on prototypes stipulated by experts, or simulated at leadership computing facilities. Such characterizations or signatures show accelerated image similarity search with real-time feedback in million-size image collections. The ability to survey samples more broadly allied to computational algorithms to compare millions of samples offers unique opportunities for deeper scientific interpretation of experiments, but also impose hurdles such as availability of storage, data transfers, large memory footprint and intensive computation. This talk discuss some strategies and software that tackles detection, segmentation and classification of materials such as carbon fibers, concrete, CMC and more.

We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3-space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are “minimally frustrated,” formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs {3, 7}, {3, 8}, {3, 9}, {3, 10}, and {3, 12} to allow embeddings in Euclidean 3-space. Nearly all of these triangulated “simplicial polyhedra” have symmetrically identical vertices, and most are chiral. The most symmetric examples include 10 infinite “deltahedra,” with equilateral triangular faces. We identify the Klein graph among the created structures.

A polynomial optimization problem (POP) is the task to minimize a multivari-
ate real polynomial given finitely polynomial inequalities as constraints. Both

systems of polynomial equations and POPs appear in countless applications in
various areas of science and engineering.
Traditionally, computational algebraic geometry deals with solving systems
of polynomial equations over the complex numbers. In the first part of my talk,
I will highlight two of the canonical approaches – Gr ̈obner bases and homotopy
continuation methods – to tackle these systems. I will also point out some of
the problems that one faces when considering real instead of complex numbers.
In the second part of the talk, I will explain how certificates of nonnegativity
can be used to attack POPs in practice. Exemplary, I will compare semidefinite
programming using the classical sums of squares (SOS) certificates with relative
entropy programming using sums of nonnegative circuit polynomials (SONC)
certificates, which were recently developed by Iliman and myself.

Auxetics are a type of metamaterial — a conventional material that has been patterned at an intermediate length scale to generate bulk material properties — that expand in all directions when exposed to uniaxial strain. Two dimensional auxetics have been studied for several decades in systems, from origami to 3D prints to linkages. Here, we propose two design schemes for realizable 3D printed three-dimensional auxetics based upon hinges. The first is a set of Lego-like interchangeable modules that combine counterrotating regular polygons with scissor mechanisms. This is guaranteed to have a one dimensional configuration space because it can be reduced to series of one degree of freedom Sarrus linkages. The second mechanism is based upon a branched cover over the simple two arm scissor mechanism which adds stability and enables force to be transferred around corners.

Thanks to the Materials Genome Initiative, there is now a database of millions of different classes of nanoporous materials, in particular zeolites. In this talk I will describe a computational approach to tackle high-throughput screening of this database to find the the best nano-porous materials for a given application, using a topological data analysis-based descriptor (TD) recognizing pore shapes. For methane storage and carbon capture applications, our method enables us to predict performance properties of zeolites. When some top-performing zeolites are known, TD can be used to efficiently detect other high-performing materials with high probability. We expect that this approach could easily be extended to other applications by simply adjusting one parameter: the size of the target gas molecule

Insights from the persistent homology analysis of porous and granular materials
Vanessa Robins (The Australian National University)

Location

MSRI: Simons Auditorium

Video

Abstract

Persistent homology is an algebraic topological tool developed for data analysis that measures changes in topology of a filtration: a growing sequence of spaces indexed by a single real parameter. It produces invariants called the barcodes or persistence diagrams that are sets of intervals recording the birth and death parameter values of each homology class in the filtration. When the filtration parameter is a length-scale, persistence diagrams provide a comprehensive description of geometric structure over the given parameter range. The physical properties of porous and granular materials critically depend on the topological and geometric details of the material micro-structure. For example, the way water flows through sandstone depends on the connectivity and diameters of its pores, and the balance of forces in a grain silo on the contacts between individual grains. These materials are therefore a natural application area for persistent homology. My work with the x-ray micro-CT group at ANU has produced topologically valid and efficient algorithms for studying and quantifying the intricate structure of complex porous materials. Our code package, diamorse, for computing skeletons, partitions, and persistence diagrams from 2D and 3D images is available on GitHub. The code contains several optimisations that allow it to process images with up to 2000^3 voxels on a high-end desktop PC. This software is enabling us to explore the connections between topology, geometry and physical properties of sandstone rock cores and granular packings. We have shown that persistence diagrams display a clear signal of crystallisation in bead packings, the degree of consolidation in sandstones, percolating length scales in porous media, and the trapping of non-wetting phase in two-phase fluid flow experiments.

This talk will explore two possible connections between random topology and circular molecules such as plasmids of DNA. One connection is through the knot which the molecule forms in space. For the knot there are two basic types of randomness to consider. If crossings are unimportant there are random walk type models yielding distributions on knots. If crossings are difficult there are models for configurations within a knot type or random walks on the set of knot types. The second connection is through the space of possible chemical species. A circular plasmid can be viewed as a map from a circle to a tiling space of short linear sequences. If a plasmid is modified chemically by homologous recombination with some collection of short circular plasmids then the short plasmids give 2-cells that can be added to the tiling space and the modifications amount to homotopies between the associated maps of circles. Thus the process is a random walk on representatives of a fixed homotopy class in the fundamental group of the linear sequence tiling space with the short plasmid 2-cells. It might be interesting to apply similar analysis to other geometries of large molecules.

Advanced materials are essential to economic and societal development, with applications in multiple industries, from clean energy, to national security, and human welfare. Traditional empirical and ‘one-at-a-time’ materials testing is unlikely to meet our future materials innovation challenges in a timely manner. Historically, novel materials exploration has been slow and expensive, taking on average 18 years from concept to commercialization. The Materials Project (www.materialsproject.org) is harnessing the power of supercomputing together with state of the art quantum mechanical theory to compute the properties of all known inorganic materials and beyond, design novel materials and offer the data for free to the community together with online analysis and design algorithms. The current release contains data derived from quantum mechanical calculations for over 80,000 materials and millions of associated properties. The software infrastructure performs thousands of calculations per week – enabling screening and predictions - for both novel solid as well as molecular species with target properties. To exemplify the approach of first-principles high-throughput materials design, we will make a deep dive into some of the ongoing work, showcasing the rapid iteration between ideas, new materials development, computations, and insight as enabled by the Materials Project infrastructure and computing resources.

Soft matter as a playground for the exploration of space partitioning
Jacob Kirkensgaard (University of Copenhagen)

Location

MSRI: Simons Auditorium

Video

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Abstract

In this talk I will give an overview of some of the remarkable structures encountered in self-assembled soft matter systems, primarily in the form of block copolymers. Block copolymers are macromolecules whose free energy minimisation is driven by an intricate competition between interfacial enthalpic contributions from domains of unlike chemical species and entropic contributions from the long-chain statistics of the polymeric molecules. A number of highlights are presented showing many novel kaleidoscopic morphologies, including 2D tiling patterns and 3D networks many of which show hierarchical features, i.e. ordering on multiple length scales.

Soap froth – the quintessential foam – is composed of polyhedral gas bubbles separated by thin liquid films. How are the bubbles shaped and how are they packed? Why do foams have a shear modulus and yield stress, which we usually associate with solids? These and other questions have been explored through simulations with the Surface Evolver, a computer program developed by Ken Brakke. We will describe foam structures ranging in complexity from perfectly ordered foams based on the Kelvin cell to random polydisperse foams with 12^3 cells in which the individual cells have a wide distribution of shapes and sizes – the former is highly idealized and the latter are very realistic. The calculations are in excellent agreement with seminal experiments by Matzke (1946) on the foam structure, and shear modulus measurements by Princen & Kiss (1986). The connection between elastic-plastic rheology and foam structure involves intermittent cascades of topological transitions; this cell-neighbor switching is a fundamental mechanism of foam flow. We will also discuss diffusive coarsening, a mechanism of foam aging, and crushing low-density solid foams with open cells.

Consistency of properties is critical for materials performance, and fundamentally depends on the microstructure on the level of the grains. The evolution of the grain structure is governed by the grain boundary energy and mobility, both functions on the five-dimensional space of grain boundary parameters. Despite decades of experimental effort, the properties of these functions in most regions of the space remain unknown. The result is that existing simulations of grain structure evolution usually employ simple analytic formulas for the grain boundary energy and mobility, and cannot quantitatively reproduce experimental grain structure evolution. Microstructure information made available by recently-developed three-dimensional microscopy techniques could soon be used to infer more realistic grain boundary energy and mobility functions. However, existing front-tracking codes generally make assumptions about the grain boundary network topology that are inconsistent with the microstructures that could arise, or restrict the allowed topological transitions to a small set that could cause substantial deviations from experimental trajectories. This talk will outline our recent efforts to substantially expand the allowed sets of grain boundary topologies and topological transitions, to formulate a physical criterion for the selection of a topological transition, and to develop equations of motion suitable for arbitrary grain boundary energies and mobilities. The intention is to prepare a front-tracking code able to perform predictive simulations of grain structure evolution on the day that realistic grain boundary energy and mobility functions become available.